Question

current skill which graph does not show a function? (four graphs with checkboxes, grid coordinate planes, pink graphs/arrows)

Explanation:

Step1: Recall the vertical line test

A graph represents a function if every vertical line intersects the graph at most once. So we check each graph with this test.

Step2: Analyze the top - left graph

This is a parabola - shaped graph. For any vertical line \(x = a\) (where \(a\) is a real number), the vertical line will intersect the parabola at most once. So it is a function.

Step3: Analyze the top - right graph

This is a graph of a triangle - like shape. If we draw a vertical line (for example, a vertical line that passes through the "middle" of the triangle), this vertical line will intersect the graph at more than one point. So it fails the vertical line test and is not a function.

Step4: Analyze the bottom - left graph

This is a piece - wise defined graph with horizontal segments. For any vertical line \(x=a\), it will intersect the graph at most once (since the segments are horizontal, a vertical line will hit at most one segment). So it is a function.

Step5: Analyze the bottom - right graph

This is a straight line (linear graph). For any vertical line \(x = a\), the vertical line will intersect the straight line at most once. So it is a function.

Answer:

The graph in the top - right (the one with the triangular - shaped pink graph) does not show a function.